On Grassmannians associated with JB*-triples

Abstract

Then Γ is a complex Lie group that has precisely n+ 1 orbits E0, . . . , En in E – each Er is the (locally closed) complex submanifold of all matrices of rank r. Clearly, Er−1 is in the closure of Er for every 1 ≤ r ≤ n and En is the unique open orbit. For every pair of integers p, q ≥ 0 let Gp,q be the Grassmannian of all p-planes in Cp+q. Then Gp,q is a compact symmetric hermitian manifold of dimension pq holomorphically equivalent to Gq,p. Every Er is in a canonical way a Γ -equivariant holomorphic fibre bundle